1.A.whether的话前面一般是“否定”,that：前面一般是肯定.
e.g：:I don't know whether he did it；
:I know that he did it.
2.A.选that的话后面就是一个陈述句,而不是一个疑问句了,显然不符合题意（由it remains a question可知）；
其实整句话可以改为：it remains a question that how we can get so much money in such a shor time.只是省略了一个that而已.所以选A.